A DC circuit has current circulating in one direction.
An AC circuit has the current reversing direction and changing in amplitude with the frequency of AC.. The magnetic field will follow.
In a DC setup the magnetic field is constant and follows the right hand rule . This is what you should use if you want something like a permanent magnet or in order to increase the strength of a permanent magnet.
In an AC setup it is continually changing :
In alternating current (AC) electromagnets, used in transformers, inductors, and AC motors and generators, the magnetic field is constantly changing. This causes energy losses in their magnetic cores that are dissipated as heat in the core.
Use AC if you want a motor, for example.
As for stronger, DC is constant, while AC is alternating and falling in amplitude in the cycle, so DC will give the stronger field, except at the peak voltage of the AC cycle, when AC will be stronger. At the RMS voltage they will be equal but maybe of opposite sign, depending on the part of the ac cycle.
In addition with DC you can use a permanent magnet for a core and thus increase the value.